This sounds very extreme. There will be truth-policers out there on this one, telling you they don't believe a word you say, but I've seen enough evidence of abusive families to know that scenarios like this one are not necessarily creative writing exercises or exaggerations. There are some sick people out there, and I've come across some equally sick stories that are not a million miles from what you've posted above.
You say your partner's 'not fussed'. That, too, isn't a surprising attitude coming from someone who grew up in such a family. They're deep in the FOG (fear, obligation and guilt) and this is the only 'normality' they've ever known.
Emotional incest, the behaviour you describe between your MiL and her son, is a real phenomenon. And this behaviour alone is enough of a red flag, even without the rest of your eye-popping laundry-list of deeply concerning behaviour. But if there's any question of exposing your child to abuse, then the only unreasonable course of action would be even to consider allowing this woman within a mile of your precious baby. In fact, I'd go so far as to suggest that Social Services intervention would be in order if you did. You have a duty to protect your child, whose welfare is far more important than this woman's feelings.
I wonder if your DP has ever had counselling in order to come to terms with these experiences? It's something that would be worth considering, if and when he's ready to face up to it. And the hardest thing in the world is to look your own life in the face and recognize this manner of abuse for what it is. It was an appalling start to life, and I'm very sorry for him.